Estimation of a precision matrix (i.e. inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence abnormal observations exacerbated in high dimensional setting as the dimensionality increases. In this work, we propose robust estimation based on an l1 regularised objective function with weighted sample matrix. robustness proposed can b...

This paper explores some connections between rank one convexity, multiplicative quasiconvexity and Schur convexity. Theorem 5.1 gives simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on the set of matrices with positive determinant. Theorem 6.2 describes a class of non-polyconvex but multiplicative quasiconvex isotropic functions. Relevance of...

The second order sequential best rotation (SBR2) algorithm was originally developed for achieving the strong decorrelation of convolutively mixed sensor array signals. It was observed that the algorithm always seems to produce spectrally majorized output signals, but this property has not previously been proven. In this work, we have taken a fresh look at the SBR2 algorithm in terms of its pote...

Force-directed layout is typically used to create organic-looking, straight-edge drawings of large graphs while combinatorial techniques are generally preferred for high-quality layout of small to medium sized graphs. In this paper we integrate edge-routing techniques into a forcedirected layout method based on constrained stress majorisation. Our basic procedure takes an initial layout for the...

We present a deterministic algorithm running in space O ? log 2 n= log logn solving the connectivity problem on strongly unambiguous graphs. In addition, we present an O(logn) time-bounded algorithm for this problem running on a parallel pointer machine.